Lectures related to Degree of a polynomial

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Generalities (conclusion)

Concludes the discussion on generalities in Chapter 3, focusing on data points, weights, and approximation methods.

Solving the Quintic: Dominant Balance

Explores dominant balance analysis in solving the quintic polynomial, with a focus on non-dimensionalization and series expansions.

Response Surfaces I: LoF and Plans

Explores lack of fit concept and experimental designs for second-degree functions.

Quadratic Approximation: Example

Covers finding the best quadratic approximation for a given function in a continuous space.

Algebra: Quadratic Trinomial

Explores quadratic trinomials, absolute values, Vieta's formulas, and graphical representation of equations.

Interpolation de degré 2 par intervalles

Explores constructing a piecewise continuous function using degree 2 interpolation by intervals.

Development Limit: Order 1 and 2

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Ordinary Differential Equations: Definitions and Solutions

Explores Ordinary Differential Equations definitions, solutions, polynomial degrees, autonomous solutions, maximal solutions, and Cauchy's problem.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Quadrature: Digital Integration

Explains quadrature formulas for digital integration and achieving accurate results.

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Mechanics of Rotational Motion

Covers the mechanics of rotational motion, including moments of inertia and energy conservation.

General Linear Recurrence Relations

Covers the solution to linear homogeneous recurrence relations with repeated roots and of arbitrary degree.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Nonparametric Regression: Kernel-Based Estimation

Covers nonparametric regression using kernel-based estimation techniques to model complex relationships between variables.

Dedekind Cuts: Rational Numbers

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Quadrature Formulas: Newton-Cotes, Lagrange Polynomials, Simpson Rule

Covers quadrature formulas, Lagrange polynomials, and the Simpson rule for accurate integration.